Lifts, transfers, and degrees of univariate maps

One can compute the local $\mathbb{A}^1$-degree at points with separable residue field by base changing, working rationally, and post-composing trace. We show that for endomorphisms of affine line, one inseparable taking a suitable lift polynomial transferring its degree. also discuss general set-up strategy in terms six functor formalism. As an application, we trace forms number fields are $\mathbb{A}^1$-degrees.